Simple diagnostics:
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To test the battery while in the vehicle, at home, with no help from Autozone...
Turn the headlights on, and crank the engine over.
If the lights are on full bright, and nearly go out when you turn the key, the battery is dead.
It might not be shot, but probably is. Batteries can do wierd things as they turn to scrap.
Usually, when a battery is simply running out of juice, the headlights will not come on full
bright.
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If the battery checks out okay, you can test the starter. (next most likely candidate)
If an automatic transmission, make sure the car is in PARK!
If standard transmission, make sure the car is in neutral!
Run a jumper cable from the positive terminal of the battery to the positive lug of the
starter motor. Touch the lug with the cable. If the starter cranks over, you know
that either the ignition switch is bad, OR the starter selonoid is bad.
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The starter solenoid has 3 or 4 wires on it. The two big heavy wires are the wire from
the battery, and the wire to the starter. (unless it is the kind that is on the starter)
One of the smaller wires is voltage from the ignition switch.
If you touch this with the jumper from the battery, it should click, and the starter
should spin.
I don't recall exactly what the 4th wire is for. (another small one)
But it can be touched with power from the battery to without harm.
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If starter motor AND the solenoid checked out okay, it could be a neutral safety switch,
OR your ignition switch. You will have to find the neutral safety switch and jumper the
terminals together. Turn the key. If the engine starts, you found the problem.
If the engine doesn't start, there is something wrong with the ignition switch.
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Since you said you hear the relay clicking, I'm assuming that is the starter solenoid making the noise.
(there are other relays for other things)
This is a good thing, in that it shows your ignition switch and selonoid are both working.
So it sure sounds like your starter is shot.
A shade tree mechanic would literally grab a small hand sledge and give it a whack.
If it is stuck, a good jolt will likely knock it loose.
This is only a temporary fix. Get it replaced.